Variable-rate universal Slepian-Wolf coding with feedback

Traditional Slepian-Wolf coding assumes known statistics and relies on asymptotically long sequences. However, in practice the statistics are unknown, and the input sequences are of finite length. In this finite regime, we must allow a non-zero probability of codeword error c and also pay a penalty by adding redundant bits in the encoding process. In this paper, we develop a universal scheme for Slepian-Wolf coding that allows encoding at variable rates close to the Slepian-Wolf limit. We illustrate our scheme in a setup where we encode a uniform Bernoulli source sequence and the second sequence, which is correlated to the first via a binary symmetric correlation channel, is available as side information at the decoder. This specific setup is easily extended to more general settings. For length n source sequences and a fixed epsilon, we show that the redundancy of our scheme is O(root n Phi(-1) (epsilon)) bits over the Slepian-Wolf limit. The prior art for Slepian-Wolf coding with known statistics shows that the redundancy is Omega (root n Phi(-1) (epsilon)). Therefore, we infer that for Slepian-Wolf coding, the penalty needed to accommodate universality is circle minus(root n Phi(-1) (epsilon)).